Who wouldn’t want to save the whales? Maybe an oilman, more interested in drilling rights than in wildlife. Or Inupiat Eskimos, whose close relationship to whales includes hunting them. Or the governor of Alaska, uneager to risk human lives to save seemingly doomed animals.

In Ken Kwapis’s “Big Miracle,” these unlikely allies find themselves doing something unexpected: trying to save three California gray whales trapped in the ice near Barrow, Alaska. Also lending hands are a Greenpeace worker, two Minnesotans with a portable de-icer, the Alaska National Guard, the Reagan administration, the Soviets and even a journalist or two.

“Big Miracle” gets off to a shaky start, but once revved up, it becomes an involving work-against-the-clock-and-the-odds action movie. Inspired by actual events from 1988, the film shows the race to save the whales and comes with a family-friendly reach-across-the-aisle message: When people put aside politics and ill will, they can accomplish something they could never manage alone.

“Big Miracle” is savvy enough to allow that many of the people pitching in do so for reasons other than altruism, and it is sentimental enough to have those characters changed by their commitment to the cause. The oilman (Ted Danson) wants the good publicity he gets from helping. He also falls in love with the whales and even finds that his nemesis, the Greenpeace activist Rachel (Drew Barrymore), isn’t so horrible after all. (Back at ya, says Rachel.) But bad things do happen. Spoiler and brace-yourself alert: the baby whale, Bamm-Bamm, doesn’t make it.

The movie halfheartedly includes a romantic-triangle plot. Adam (a warm John Krasinski), the journalist who breaks the whale story, has a crush on a Los Angeles newscaster (Kristen Bell) covering it too. Adam is also Rachel’s ex. But mostly “Big Miracle” sticks to the rescue tale.

Sometimes the attention focused on this problem in a small corner of Alaska can seem far-fetched, but Mr. Kwapis reminds us that it really happened by cutting in period footage of Dan Rather and Tom Brokaw delivering updates. The plausibility meter swings the other way when President Reagan, seen from the back, starts a phone conversation with Mikhail S. Gorbachev like this: “Gorby? It’s Ronnie.” Gorby, though, is fine with it: he sends a Soviet ice-breaking vessel to help.